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A Dirichlet process mixture regression model for the analysis of competing risk events Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2024-02-24 Francesco Ungolo, Edwin R. van den Heuvel
We develop a regression model for the analysis of competing risk events. The joint distribution of the time to these events is flexibly characterized by a random effect which follows a discrete probability distribution drawn from a Dirichlet Process, explaining their variability. This entails an additional layer of flexibility of this joint model, whose inference is robust with respect to the misspecification
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Optimal payout strategies when Bruno de Finetti meets model uncertainty Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2024-02-21 Yang Feng, Tak Kuen Siu, Jinxia Zhu
Model uncertainty is ubiquitous and plays an important role in insurance and financial modeling. While a substantial effort has been given to studying optimal consumption, portfolio selection and investment problems in the presence of model uncertainty, relatively little attention is given to investigating optimal payout policies taking account of the impacts of model uncertainty. As one of the early
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Can price collars increase insurance loss coverage? Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2024-02-15 Indradeb Chatterjee, MingJie Hao, Pradip Tapadar, R. Guy Thomas
Loss coverage, defined as expected population losses compensated by insurance, is a public policy criterion for comparing different risk-classification regimes. Using a model with two risk-groups (high and low) and iso-elastic demand, we compare loss coverage under three alternative regulatory regimes: (i) full risk-classification (ii) pooling (iii) a price collar, whereby each insurer is permitted
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Inter-order relations between equivalence for L-quantiles of the Student's t distribution Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2024-02-13 Valeria Bignozzi, Luca Merlo, Lea Petrella
In the statistical and actuarial literature, -quantiles, , represent an important class of risk measures defined through an asymmetric -power loss function that generalize the classical (-)quantiles. By exploiting inter-order relations between partial moments, we show that for a Student's distribution with degrees of freedom the -quantile and the -quantile always coincide for any . For instance, for
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Random distortion risk measures Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2024-02-12 Xin Zang, Fan Jiang, Chenxi Xia, Jingping Yang
This paper presents one type of random risk measures, named as the random distortion risk measure. The random distortion risk measure is a generalization of the traditional deterministic distortion risk measure by randomizing the deterministic distortion function and the risk distribution respectively, where a stochastic distortion is introduced to randomize the distortion function, and a sub--algebra
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Scenario selection with LASSO regression for the valuation of variable annuity portfolios Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2024-02-07 Hang Nguyen, Michael Sherris, Andrés M. Villegas, Jonathan Ziveyi
Variable annuities (VAs) are increasingly becoming popular insurance products in many developed countries which provide guaranteed forms of income depending on the performance of the equity market. Insurance companies often hold large VA portfolios and the associated valuation of such portfolios for hedging purposes is a very time-consuming task. There have been several studies focusing on inventing
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A Hawkes model with CARMA(p,q) intensity Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2024-02-02 Lorenzo Mercuri, Andrea Perchiazzo, Edit Rroji
In this paper we introduce a new model, named CARMA(p,q)-Hawkes, as the Hawkes model with exponential kernel implies a strictly decreasing behavior of the autocorrelation function while empirical evidences reject its monotonicity. The proposed model is a Hawkes process where the intensity follows a Continuous Time Autoregressive Moving Average (CARMA) process. We also study the conditions for the stationarity
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Efficient algorithms for calculating risk measures and risk contributions in copula credit risk models Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2024-01-23 Zhenzhen Huang, Yue Kuen Kwok, Ziqing Xu
This paper innovates in the risk management of insurance and banking capital by exploring efficient, accurate, and reliable algorithms for evaluating risk measures and contributions in copula credit risk models. We propose a hybrid saddlepoint approximation algorithm, which leverages a synergy of nice analytical tractability from the saddlepoint approximation framework and efficient numerical integration
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Pricing guaranteed annuity options in a linear-rational Wishart mortality model Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2024-01-22 José Da Fonseca
This paper proposes a new model, the linear-rational Wishart model, which allows the joint modelling of mortality and interest rate risks. Within this framework, we obtain closed-form solutions for the survival bond and the survival floating rate bond. We also derive a closed-form solution for the guaranteed annuity option, i.e., an option on a sum of survival (floating rate) bonds, which can be computed
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Bootstrap consistency for the Mack bootstrap Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2024-01-17 Julia Steinmetz, Carsten Jentsch
Mack's distribution-free chain ladder reserving model belongs to the most popular approaches in non-life insurance mathematics. Proposed to determine the first two moments of the reserve, it does not allow to identify the whole distribution of the reserve. For this purpose, Mack's model is usually equipped with a tailor-made bootstrap procedure. Although widely used in practice to estimate the reserve
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Moral hazard in loss reduction and state-dependent utility Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2024-01-17 S. Hun Seog, Jimin Hong
We consider a state-dependent utility model with a binary loss distribution, wherein moral hazard occurs in loss reduction. The findings are as follows: First, partial insurance is optimal under state-dependent utility. Second, the optimal insurance coverage and effort level are affected by the relative sizes of the marginal utilities in the loss and no-loss states. (i) If the marginal utilities are
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Bowley solution under the reinsurer's default risk Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2024-01-11 Yanhong Chen, Ka Chun Cheung, Yiying Zhang
In this paper, we examine how a monopolistic reinsurer designs a Bowley reinsurance contract, under the assumption that the reinsurer will default on payment if the compensated loss exceeds the sum of the initial capital and the premium charged from the contract. The problem is divided into two subproblems faced by the insurer and the reinsurer in turn. The optimal reinsurance contract is analyzed
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Tweedie multivariate semi-parametric credibility with the exchangeable correlation Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2024-01-11 Himchan Jeong
This article proposes a framework for determining credibility premiums for multiple coverages in a compound risk model with Tweedie distribution. The framework builds upon previous results on credibility premium and provides an explicit multivariate credibility premium formula that is applicable to the Tweedie family assuming that the unobserved heterogeneity for the multiple coverage have the common
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Probability equivalent level for CoVaR and VaR Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2024-01-10 Patricia Ortega-Jiménez, Franco Pellerey, Miguel A. Sordo, Alfonso Suárez-Llorens
For a given risk, the well-known classical definition of Value-at-Risk (VaR) does not take into account possible interactions with other observable risks. For this reason, conditional VaRs that capture contagion effects and tail dependence among risks, such as the Co-Value-at-Risk (CoVaR), have been defined and studied in recent literature. In this paper we study conditions that guarantee, in the bivariate
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Variance insurance contracts Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2024-01-09 Yichun Chi, Xun Yu Zhou, Sheng Chao Zhuang
We study the design of an optimal insurance contract in which the insured maximizes her expected utility and the insurer limits the variance of his risk exposure while maintaining the principle of indemnity and charging the premium according to the expected value principle. We derive the optimal policy semi-analytically, which is coinsurance above a deductible when the variance bound is binding. This
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Adjusted higher-order expected shortfall Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2024-01-02 Zhenfeng Zou, Taizhong Hu
How to detect different tail behaviors of two risk random variables with the same mean is an important task. In this paper, motivated by Burzoni et al. (2022), a class of convex risk measures, referred to as adjusted higher-order Expected Shortfall (ES), is introduced and studied. The adjusted risk measure quantifies risk as the minimum amount of capital that has to be raised and injected into a financial
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On the factors determining the health profiles and care needs of institutionalized elders Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2023-12-19 Aleksandr Shemendyuk, Joël Wagner
In many developed countries, population aging raises a number of issues related to the organization and financing of long-term care. While the determinants of the overall burden and cost of care are well understood, the organization of institutionalized long-term care must meet the needs of the elderly. One way to optimize management is to use information on health problems to assess the infrastructure
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A family of variability measures based on the cumulative residual entropy and distortion functions Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2023-12-13 Georgios Psarrakos, Abdolsaeed Toomaj, Polyxeni Vliora
Variability measures are important tools in the construction of premium principles and risk aversions. In this paper, we propose a family of such measures based on a distorted weighted cumulative residual entropy, which follows by a sensitivity analysis of distortion risk measures. For this family, we obtain properties, connections with other measures, a covariance representation, and some useful interpretations
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Optimal investment in defined contribution pension schemes with forward utility preferences Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2023-12-13 Kenneth Tsz Hin Ng, Wing Fung Chong
Optimal investment strategies of an individual worker during the accumulation phase in the defined contribution pension scheme have been well studied in the literature. Most of them adopted the classical backward model and approach, but any pre-specifications of retirement time, preferences, and market environment models do not often hold in such a prolonged horizon of the pension scheme. Pre-commitment
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Longevity hedge effectiveness using socioeconomic indices Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2023-12-12 Malene Kallestrup-Lamb, Nicolai Søgaard Laursen
This paper evaluates socioeconomic basis risk in longevity hedging. Using data for a full population stratified into socioeconomic groups, we explore the benefits and costs of two alternative hedging strategies, with and without basis risk, in the capital market. The benefit of the longevity hedge is represented by the risk reduction in the variability of a life annuity, whereas the cost is the notional
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Optimal annuitization and asset allocation under linear habit formation Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2023-12-07 Guohui Guan, Zongxia Liang, Xingjian Ma
This paper studies the optimal consumption-investment-annuitization problem for a retiree with linear consumption habits. We explore the effect of consumption habits on the decision to annuitize when annuities are purchased as a lump sum. The problem is formulated as a combined stopping-control problem. We derive optimal annuitization time, investment, and consumption strategies by a generalized dual
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A multi-agent incomplete equilibrium model and its applications to reinsurance pricing and life-cycle investment Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2023-11-30 Keisuke Kizaki, Taiga Saito, Akihiko Takahashi
This paper develops an incomplete equilibrium model with multi-agents' different risk attitudes and heterogeneous income/payout profiles. Particularly, we apply its concrete and computationally tractable model to reinsurance derivatives pricing and life-cycle investment, which are important for insurance and asset management companies in practice. In numerical experiments, we explicitly obtain endogenously
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Bayesian CART models for insurance claims frequency Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2023-11-30 Yaojun Zhang, Lanpeng Ji, Georgios Aivaliotis, Charles Taylor
The accuracy and interpretability of a (non-life) insurance pricing model are essential qualities to ensure fair and transparent premiums for policy-holders, that reflect their risk. In recent years, classification and regression trees (CARTs) and their ensembles have gained popularity in the actuarial literature, since they offer good prediction performance and are relatively easy to interpret. In
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Time-consistent reinsurance-investment games for multiple mean-variance insurers with mispricing and default risks Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2023-11-27 Yang Yang, Guojing Wang, Jing Yao
This paper studies a non-zero-sum stochastic differential game for multiple mean-variance insurers. Insurers can purchase proportional reinsurance and invest in a risk-free asset, a market index, a defaultable bond and multiple pairs of mispriced stocks. The dynamics of the mispriced stocks satisfy a “cointegrated system” where the expected returns follow the mean reverting processes, and the bond
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Asymptotic Results on Tail Moment for Light-tailed Risks Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2023-11-21 Bingjie Wang, Jinzhu Li
In this paper, we focus on the asymptotic behavior of a recently popular risk measure called the tail moment (TM), which has been extensively applied in the field of risk theory. We conduct the study under the framework in which the individual risks of a financial or insurance system follow convolution equivalent or Gamma-like distributions. Precise asymptotic results are obtained for the TM when the
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Stressing dynamic loss models Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2023-11-22 Emma Kroell, Silvana M. Pesenti, Sebastian Jaimungal
Stress testing, and in particular, reverse stress testing, is a prominent exercise in risk management practice. Reverse stress testing, in contrast to (forward) stress testing, aims to find an alternative but plausible model such that under that alternative model, specific adverse stresses (i.e. constraints) are satisfied. Here, we propose a reverse stress testing framework for dynamic models. Specifically
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Fitting Tweedie's compound Poisson model to pure premium with the EM algorithm Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2023-11-17 Guangyuan Gao
We consider the situation when the number of claims is unavailable, and a Tweedie's compound Poisson model is fitted to the observed pure premium. Currently, there are two different models based on the Tweedie distribution: a single generalized linear model (GLM) for mean and a double generalized linear model (DGLM) for both mean and dispersion. Although the DGLM approach facilitates the heterogeneous
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Risk-neutral valuation of GLWB riders in variable annuities Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2023-11-09 Anna Rita Bacinello, Rosario Maggistro, Ivan Zoccolan
In this paper we propose a model for pricing GLWB variable annuities under a stochastic mortality framework. Our set-up is very general and only requires the Markovian property for the mortality intensity and the asset price processes. The contract value is defined through an optimization problem which is solved by using dynamic programming. We prove, by backward induction, the validity of the bang-bang
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Analyzing the interest rate risk of equity-indexed annuities via scenario matrices Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2023-11-08 Sascha Günther, Peter Hieber
The financial return of equity-indexed annuities depends on an underlying fund or investment portfolio complemented by an investment guarantee. We discuss a so-called cliquet-style or ratchet-type guarantee granting a minimum annual return. Its path-dependent payoff complicates valuation and risk management, especially if interest rates are modelled stochastically. We develop a novel scenario-matrix
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Diagnostic tests before modeling longitudinal actuarial data Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2023-09-20 Yinhuan Li, Tsz Chai Fung, Liang Peng, Linyi Qian
In non-life insurance, it is essential to understand the serial dynamics and dependence structure of the longitudinal insurance data before using them. Existing actuarial literature primarily focuses on modeling, which typically assumes a lack of serial dynamics and a pre-specified dependence structure of claims across multiple years. To fill in the research gap, we develop two diagnostic tests, namely
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Optimal risk management with reinsurance and its counterparty risk hedging Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2023-09-19 Yichun Chi, Tao Hu, Yuxia Huang
In this paper, we revisit the study of an optimal risk management strategy for an insurer who wants to maximize the expected utility by purchasing reinsurance and managing reinsurance counterparty risk with a default-free hedging instrument, where the reinsurance premium is calculated by the expected value principle and the price of the hedging instrument equals the expected payoff plus a proportional
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Two-phase selection of representative contracts for valuation of large variable annuity portfolios Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2023-09-14 Ruihong Jiang, David Saunders, Chengguo Weng
A computationally appealing methodology for the valuation of large variable annuities portfolios is a metamodelling framework that evaluates a small set of representative contracts, fits a predictive model based on these computed values, and then extrapolates the model to estimate the values of the remaining contracts. This paper proposes a new two-phase procedure for selecting representative contracts
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Robust optimal asset-liability management with mispricing and stochastic factor market dynamics Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2023-09-12 Ning Wang, Yumo Zhang
This paper investigates a robust optimal asset-liability management problem under an expected utility maximization criterion. More specifically, the manager is concerned about the potential model uncertainty and aims to seek the robust optimal investment strategies. We incorporate an uncontrollable random liability described by a generalized drifted Brownian motion. Also, the manager has access to
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IME's Editorial Board Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2023-09-07 Rob Kaas, Roger J.A. Laeven, Sheldon Lin, Qihe Tang, Gordon Willmot, Hailiang Yang
Abstract not available
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European option pricing with market frictions, regime switches and model uncertainty Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2023-09-04 Tak Kuen Siu
The impact of market frictional costs on pricing insurance and financial products in a regime-switching environment has not been well-explored. This paper introduces a general pricing model for European options which incorporates market frictional costs, regime switches and model uncertainty. Regime switches are due to changes in an economic environment. Model uncertainty is attributed to misspecification
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Bivariate distribution regression with application to insurance data Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2023-09-01 Yunyun Wang, Tatsushi Oka, Dan Zhu
Understanding variable dependence, particularly eliciting their statistical properties given a set of covariates, provides the mathematical foundation in practical operations management such as risk analysis and decision-making given observed circumstances. This article presents an estimation method for modeling the conditional joint distribution of bivariate outcomes based on the distribution regression
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Diversification quotients based on VaR and ES Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2023-09-01 Xia Han, Liyuan Lin, Ruodu Wang
The diversification quotient (DQ) is recently introduced for quantifying the degree of diversification of a stochastic portfolio model. It has an axiomatic foundation and can be defined through a parametric class of risk measures. Since the Value-at-Risk (VaR) and the Expected Shortfall (ES) are the most prominent risk measures widely used in both banking and insurance, we investigate DQ constructed
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Intergenerational actuarial fairness when longevity increases: Amending the retirement age Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2023-09-01 Jorge M. Bravo, Mercedes Ayuso, Robert Holzmann, Edward Palmer
Continuous longevity improvements and population ageing have led countries to modify national public pension schemes by increasing standard and early retirement ages in a discretionary, scheduled, or automatic way, and making it harder for people to retire prematurely. To this end, countries have adopted alternative retirement age strategies, but our analyses show that the measures taken are often
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Intergenerational sharing of unhedgeable inflation risk Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2023-08-30 Damiaan H.J. Chen, Roel M.W.J. Beetsma, Sweder J.G. van Wijnbergen
We explore how members of a collective pension scheme can share inflation risks in the absence of suitable financial market instruments. Using intergenerational risk-sharing arrangements, risks can be allocated better across the scheme's participants than would be the case in a strictly individual- or cohort-based pension scheme, as these can only lay off risks via existing financial market instruments
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Joint life care annuities to help retired couples to finance the cost of long-term care Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2023-08-28 Manuel Ventura-Marco, Carlos Vidal-Meliá, Juan Manuel Pérez-Salamero González
This paper examines the possibility of including cash-for-care benefits in life care annuities (LCAs) to help retired couples to cope with the cost of long-term care (LTC). The paper develops an actuarial model to assess how much it would cost to add an extra stream of payments to annuities for couples should either or both require LTC. We also analyse how willing couples would be to choose this type
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Multi-constrained optimal reinsurance model from the duality perspectives Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2023-08-28 Ka Chun Cheung, Wanting He, He Wang
In the presence of multiple constraints such as the risk tolerance constraint and the budget constraint, many extensively studied (Pareto-)optimal reinsurance problems based on general distortion risk measures become technically challenging and have only been solved using ad hoc methods for certain special cases. In this paper, we extend the method developed in Lo (2017a) by proposing a generalized
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Hedging longevity risk under non-Gaussian state-space stochastic mortality models: A mean-variance-skewness-kurtosis approach Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2023-08-19 Johnny Siu-Hang Li, Yanxin Liu, Wai-Sum Chan
Longevity risk has recently become a high profile risk among insurers and pension plan sponsors. One way to mitigate longevity risk is to build a hedge using derivatives that are linked to mortality indexes. Longevity hedging methods are often based on the normality assumption, considering only the variance but no other (higher) moments. However, strong empirical evidence suggests that mortality improvement
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Aggregate Markov models in life insurance: Properties and valuation Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2023-08-07 Jamaal Ahmad, Mogens Bladt, Christian Furrer
In multi-state life insurance, an adequate balance between analytic tractability, computational efficiency, and statistical flexibility is of great importance. This might explain the popularity of Markov chain modelling, where matrix analytic methods allow for a comprehensive treatment. Unfortunately, Markov chain modelling is unable to capture duration effects, so this paper presents aggregate Markov
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Optimal investment, consumption and life insurance purchase with learning about return predictability Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2023-08-07 Xingchun Peng, Baihui Li
This paper studies the optimal investment, consumption and life insurance purchase problem for a wage earner under the condition that the return on the risky asset is predictable. We assume that the market price of risk is an affine function consisting of an observable and an unobservable factor that follow the O-U processes, while the evolution of the interest rate is described by the Vasicek model
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Optimal risk sharing and dividend strategies under default contagion: A semi-analytical approach Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2023-08-01 Ming Qiu, Zhuo Jin, Shuanming Li
We investigate the risk control and dividend optimization problem of an insurance group in a general setting and propose an innovative semi-analytical approach to the problem. The group consists of multiple subsidiaries and is subject to exogenous default risk. The default intensity is subject to the contagious effect. The contagious effect refers to the increase in default intensities of surviving
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Valuation of general GMWB annuities in a low interest rate environment Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2023-07-27 Claudio Fontana, Francesco Rotondi
Variable annuities with Guaranteed Minimum Withdrawal Benefits (GMWB) entitle the policy holder to periodic withdrawals together with a terminal payoff linked to the performance of an equity fund. In this paper, we consider the valuation of a general class of GMWB annuities, allowing for step-up, bonus and surrender features, taking also into account mortality risk and death benefits. When dynamic
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Equilibria and efficiency in a reinsurance market Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2023-07-28 Michael B. Zhu, Mario Ghossoub, Tim J. Boonen
We study equilibria in a reinsurance market with multiple reinsurers that are endowed with heterogeneous beliefs, where preferences are given by distortion risk measures, and pricing is done via Choquet integrals. We construct a model in the form of a sequential economic game, where the reinsurers have the first-mover advantage over the insurer, as in the Stackelberg setting. However, unlike the Stackelberg
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Asymptotics for a time-dependent by-claim model with dependent subexponential claims Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2023-07-17 Meng Yuan, Dawei Lu
Consider a by-claim risk model with a constant force of interest, where each main claim may induce a by-claim after a random time. We propose a time-claim-dependent framework, that incorporates dependence between not only the waiting time and the claim but also the main claim and the corresponding by-claim. Based on this framework, we derive some asymptotic estimates for the finite-time ruin probabilities
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Corrigendum and addendum to “Range Value-at-Risk bounds for unimodal distributions under partial information” [Insurance: Math. Econ. 94 (2020) 9–24] Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2023-07-13
In Section 2 of Bernard et al. (2020), we study bounds on Range Value-at-Risk under the assumption of non-negative risk. However, Proposition 3 is erroneous, and hence Theorems 3, 4, and 5 and Corollary 5 are no longer valid. In this corrigendum, we provide a direct replacement of these theorems and corollary. We note that these results provide generalizations in that there is no longer a constraint
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Annuitizing at a bounded, absolutely continuous rate to minimize the probability of lifetime ruin Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2023-06-26 Xiaoqing Liang, Virginia R. Young
We minimize the probability of lifetime ruin in a deterministic financial and insurance model, although the investor's time of death is random, with an age-dependent force of mortality. By contrast with the traditional anything-anytime annuitization model (that is, individuals can annuitize any fraction of their wealth at anytime), the individual only purchases life annuity income gradually, using
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A note on portfolios of averages of lognormal variables Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2023-06-24 Phelim Boyle, Ruihong Jiang
This paper establishes conditions under which a portfolio consisting of the averages of K blocks of lognormal variables converges to a K-dimensional lognormal variable as the number of variables in each block increases. The associated block covariance matrix has to have a special structure where the correlations and variances within the block submatrices are equal. We show why the variance homogeneity
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Optimal insurance design under mean-variance preference with narrow framing Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2023-06-21 Xiaoqing Liang, Wenjun Jiang, Yiying Zhang
In this paper, we study an optimal insurance design problem under mean-variance criterion by considering the local gain-loss utility of the net payoff of insurance, namely, narrow framing. We extend the existing results in the literature to the case where the decision maker has mean-variance preference with a constraint on the expected utility of the net payoff of insurance, where the premium is determined
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Optimal retirement savings over the life cycle: A deterministic analysis in closed form Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2023-06-07 Marcel Fischer, Bjarne Astrup Jensen, Marlene Koch
In this paper, we explore the life cycle consumption-savings problem in a stylized model with a risk-free investment opportunity, a tax-deferred retirement account, and deterministic labor income. Our closed form solutions show that liquidity constraints can be severely binding; in particular in situations with a high growth rate of labor income, in which retirement saving is optimally postponed. With
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Multiple per-claim reinsurance based on maximizing the Lundberg exponent Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2023-06-05 Hui Meng, Li Wei, Ming Zhou
In this paper, we consider the optimal per-claim reinsurance problem for an insurer who designs a reinsurance contract with multiple reinsurance participants. In contrast to using the value-at-risk as a short-term risk measure, we take the Lundberg exponent in risk theory as a risk measure for the insurer over a long-term horizon because the Lundberg upper bound performs better in measuring the infinite-time
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Conditional mean risk sharing of losses at occurrence time in the compound Poisson surplus model Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2023-06-01 Michel Denuit, Christian Y. Robert
This paper proposes a new risk-sharing procedure, framed into the classical insurance surplus process. Compared to the standard setting where total losses are shared at the end of the period, losses are allocated among participants at their occurrence time in the proposed model. The conditional mean risk-sharing rule proposed by Denuit and Dhaene (2012) is applied to this end. The analysis adopts two
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The Cramér-Lundberg model with a fluctuating number of clients Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2023-05-30 Peter Braunsteins, Michel Mandjes
This paper considers the Cramér-Lundberg model, with the additional feature that the number of clients can fluctuate over time. Clients arrive according to a Poisson process, where the times they spend in the system form a sequence of independent and identically distributed non-negative random variables. While in the system, every client generates claims and pays premiums. In order to describe the
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Pairwise counter-monotonicity Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2023-05-29 Jean-Gabriel Lauzier, Liyuan Lin, Ruodu Wang
We systematically study pairwise counter-monotonicity, an extremal notion of negative dependence. A stochastic representation and an invariance property are established for this dependence structure. We show that pairwise counter-monotonicity implies negative association, and it is equivalent to joint mix dependence if both are possible for the same marginal distributions. We find an intimate connection
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On the area in the red of Lévy risk processes and related quantities Insurance: Mathematics and Economics (IF 1.9) Pub Date : 2023-05-19 Mohamed Amine Lkabous, Zijia Wang
Under contemporary insurance regulatory frameworks, an insolvent insurer placed in receivership may have the option of rehabilitation, during which a plan is devised to resolve the insurer's difficulties. The regulator and receiver must analyze the company's financial condition and determine whether a rehabilitation is likely to be successful or if its problems are so severe that the appropriate action